zbMATH — the first resource for mathematics

Exact flow of a third grade fluid past a porous plate using homotopy analysis method. (English) Zbl 1211.76076
Summary: The flow of a third grade fluid past a porous plate is considered. An exact analytical solution of the governing non-linear differential equation is constructed using homotopy analysis method. It is observed that the relevant perturbation solution corresponds to a special case of the presented solution.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76S05 Flows in porous media; filtration; seepage
76A05 Non-Newtonian fluids
Full Text: DOI
[1] Truesdal, C.; Noll, W., The non-linear field theories of mechanics, () · Zbl 0779.73004
[2] Rajagopal, K.R.; Na, T.Y., On stokes’ problem for a non-Newtonian fluid, Acta mech., 48, 233-239, (1983) · Zbl 0528.76003
[3] Erdogan, M.E., Plane surface suddenly set in motion in a non-Newtonian fluid, Acta mech., 108, 179-187, (1995) · Zbl 0846.76006
[4] Siddiqui, A.M.; Kaloni, P.N., Plane steady flows of a third grade fluid, Int. J. engng. sci., 25, 171-188, (1987) · Zbl 0615.76007
[5] Molloica, F.; Rajagopal, K.R., Secondary flows due to axial shearing of third grade fluid between two eccentrically placed cylinders, Int. J. engng. sci., 37, 411-429, (1999) · Zbl 1210.76017
[6] Hayat, T.; Nadeem, S.; Asghar, S.; Siddiqui, A.M., MHD rotating flow of a third grade fluid on an oscillating porous plate, Acta mech., 152, 177-190, (2001) · Zbl 0993.76091
[7] S.J. Liao, A kind of linearity-invariance under homotopy and some simple applications of it in mechanics. Report No. 520, Institute of Shipbuilding, University of Hamburg, 1992
[8] Liao, S.J., Application of process analysis method in solution of 2D non-linear progressive gravity waves, J. ship res., 36, 30-37, (1992)
[9] Liao, S.J., Higher-order stream function-vorticity formulation of 2D navier – stokes equations, Int. J. numer. meth. fluids, 15, 595-612, (1992) · Zbl 0762.76063
[10] Liao, S.J., A second-order approximate analytical solution of a simple pendulum by the process analysis method, J. appl. mech., 59, 970-975, (1992) · Zbl 0769.70017
[11] Liao, S.J., An approximate solution technique not depending on small parameters: A special example, Int. J. non-linear mech., 30, 371-380, (1995) · Zbl 0837.76073
[12] Wang, Z.K.; Kao, T.A., An introduction to homotopy methods, (1991), Chongqing Publishing House Chongqing
[13] Duld, A., Lectures on algebraic topology, (1972), Springer-Verlag Berlin Heidelberg
[14] Papy, G., Topologie als grundlage des analysis-unterrichts, (1970), Vandenhoich and Ruprecht Gottingen
[15] Nash, C.; Sen, S., Topology and geometry for physicists, (1983), Academic Press, Inc London · Zbl 0529.53001
[16] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of non-linear equations in several variables, (1970), Academic press New York · Zbl 0241.65046
[17] Liao, S.J., An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude, Int. J. non-linear mech., 38, 1173-1183, (2003) · Zbl 1348.74225
[18] Liao, S.J.; Cheung, K.F., Homotopy analysis of non-linear progressive waves in deep water, J. engng. math., 45, 105-116, (2003) · Zbl 1112.76316
[19] Wang, C.; Zhu, J.M.; Liao, S.J.; Pop, I., On the explicit analytic solution of cheng chang equation, Int. J. heat mass transf., 46, 1855-1860, (2003) · Zbl 1029.76050
[20] Liao, S.J.; Campo, A., Analytic solutions of the temperature distribution in Blasius viscous flow problems, J. fluid mech., 453, 411-425, (2002) · Zbl 1007.76014
[21] Liao, S.J., An analytic approximation of the drag coefficient for the viscous flow past a sphere, Int. J. non-linear mech., 37, 1-18, (2002) · Zbl 1116.76335
[22] Liao, S.J., An explicit, totally analytic approximation of Blasius viscous flow problems, Int. J. non-linear mech., 34, 759-778, (1999) · Zbl 1342.74180
[23] Liao, S.J., A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate, J. fluid mech., 385, 101-128, (1999) · Zbl 0931.76017
[24] Liao, S.J.; Chwang, A.T., Application of homotopy analysis method in non-linear oscillations, J. appl. mech., 65, 914-992, (1998)
[25] Liao, S.J., An approximate solution technique which does not depend upon small parameters (part II) an application in fluid mechanics, Int. J. non-linear mech., 32, 815-822, (1997) · Zbl 1031.76542
[26] Rivlin, R.S.; Ericksen, J.L., Stress deformation relations for isotropic materials, J. rat. mech. anal., 4, 323-425, (1955) · Zbl 0064.42004
[27] Fosdick, R.L.; Rajagopal, K.R., Thermodynamics and stability of fluids of third grade, Proc. R. soc. lond. A, 369, 351-377, (1980) · Zbl 0441.76002
[28] Dunn, J.E.; Fosdick, R.L., Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. rat. mech. anal., 56, 191-252, (1974) · Zbl 0324.76001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.